Question

What is the value of a?

Answer 1

Answer:

6√2

Step-by-step explanation:

ΔEBD and ΔEDC are similar. Therefore the sides are in proportion:

$\dfrac{DE}{EB}=\dfrac{EC}{DE}$

We have:

DE = a

EB = 18

EC = 4

Substitute:

$\dfrac{a}{18}=\dfrac{4}{a}$            cross multiply

$(a)(a)=(18)(4)\\\\a^2=72\to a=\sqrt{72}\\\\a=\sqrt{36\cdot2}\\\\a=\sqrt{36}\cdot\sqrt2\\\\a=6\sqrt2$

Answer 2

Answer:

a^2 = 18 * 4

a^2 = 72

a = 6√2